Question: Given $ m \angle QPR = 3x + 14$, and $ m \angle RPS = 5x + 62$, find $m\angle QPR$. $P$ $Q$ $S$ $R$
Explanation: From the diagram, we see that together ${\angle QPR}$ and ${\angle RPS}$ form ${\angle QPS}$ , so $ {m\angle QPR} + {m\angle RPS} = {m\angle QPS}$ Since $\angle QPS$ is a straight angle, we know ${m\angle QPS = 180}$ Substitute in the expressions that were given for each measure: $ {3x + 14} + {5x + 62} = {180}$ Combine like terms: $ 8x + 76 = 180$ Subtract $76$ from both sides: $ 8x = 104$ Divide both sides by $8$ to find $x$ $ x = 13$ Substitute $13$ for $x$ in the expression that was given for $m\angle QPR$ $ m\angle QPR = 3({13}) + 14$ Simplify: $ {m\angle QPR = 39 + 14}$ So ${m\angle QPR = 53}$.